Solving the heptic by iteration in two dimensions: Geometry and dynamics under Klein's group of order 168

There is a family of seventh-degree polynomials $H$ whose members
possess the symmetries of a simple group of order $168$. This group
has an elegant action on the complex projective plane. Developing
some of the action's rich algebraic and geometric properties rewards
us with a special map that also realizes the $168$-fold symmetry.
The map's dynamics provides the main tool in an algorithm that
solves certain "heptic" equations in $H$.

Citation:
Scott Crass. Solving the heptic by iteration in two dimensions: Geometry and dynamics under Klein's group of order 168. Journal of Modern Dynamics,
2007, 1
(2)
: 175-203.
doi: 10.3934/jmd.2007.1.175